1. Field
The presently disclosed subject matter relates to an optical deflector used in a projector, a headlamp, a bar code reader, a laser printer, a laser head amplifier, a head-up display unit and the like, and its designing method.
2. Description of the Related Art
FIG. 1A is a perspective view illustrating a first prior art one-dimensional optical deflector, and FIG. 1B is a partial enlargement of the optical deflector of FIG. 1A enclosed by a dotted line B in FIG. 1A (see: FIG. 5 of JP2008-20701A).
As illustrated in FIGS. 1A and 1B, the first prior art one-dimensional optical deflector is constructed by a circular mirror 1, a pair of torsion bars 2a and 2b oppositely arranged along a Y-axis (rocking axis) each having an end coupled to the circumference of the mirror 1, a pair of semi-circular piezoelectric actuators 3-1 and 3-2 opposite to each other with respect to the mirror 1 each coupled to both of the torsion bars 2a and 2b for rocking the mirror 1 around the Y-axis, a rectangular fixed frame 4 surrounding the semi-circular piezoelectric actuators 3-1 and 3-2 each including one piezoelectric portion 3-11 (3-21) made of lead titanate zirconate PbZrTi02 (PZT), and a pair of coupling bars 5-1 and 5-2 arranged along an X-axis perpendicular to the Y-axis having ends coupled to the inner circumference of the fixed frame 4 and other ends coupled to the outer circumference of the semi-circular piezoelectric actuators 3-1 and 3-2.
In FIGS. 1A and 1B, in a resonance state, when the rocking frequency “f” of the semi-circular piezoelectric actuators 3-1 and 3-2 is close to the natural frequency of a mechanically-vibrating system of the mirror 1, the rocking angle of the mirror 1 with respect to the Y-axis can be increased.
In the above-mentioned resonance state, the inventors found that, portions of the semi-circular piezoelectric actuators 3-1 and 3-2 where the torsion bars 2a and 2b and the coupling bars 5-1 and 5-2 are coupled form loops having maximum amplitudes of a resonant vibration, while portions of the semi-circular piezoelectric actuators 3-1 and 3-2 having 45°-angled diameter directions with respect to a diameter line between the torsion bars 2a and 2b and a diameter line between the coupling bars 5-1 and 5-2 form nodes having essentially zero amplitudes of the resonant vibration.
The loop portions and node portions of the semi-circular piezoelectric actuators 3-1 and 3-2 are discussed in more detail below.
In FIG. 1B, radial axes C1, C2, . . . , C16 are defined at intervals 22.5° centered at a point “0” on a plane of the fixed frame 4. Also, a circumferential line L is defined at a center line between the outer and inner circumferences of the semi-circular piezoelectric actuators 3-1 and 3-2. Further, P1, P2, . . . , P16 are defined as locations at intersections between the circumferential line L and the radial axes C1, C2, . . . , C16, respectively.
The X-axis is defined as the direction of the radial axis C5, and the Y-axis is defined as the direction of the radial axis C1. In this case, the Y-axis is shifted from the rocking direction of the mirror 1 by a half thickness of the mirror 1; however, since this half thickness is very thin, the Y-axis is substantially the same as the rocking direction of the mirror 1. Also, a Z-axis is defined as a direction perpendicular to the X-axis and the Y-axis.
In FIG. 2, which illustrates the amplitudes at the locations P9, P10, P11, P12 and P13 along the Z-axis of FIG. 1B in a resonant state whose resonant frequency is 18.877 kHz, three or four amplitudes at three or four X-coordinate values and at one Y-coordinate value were measured. As illustrated in FIG. 2, the amplitude at the location P9 was about 4.4 mm, the amplitude at the location P10 was about 1.6 mm, the amplitude at the location P11 was about 0.3 mm, the amplitude at the location P12 was about 1.5 mm, and the amplitude at the location P13 was about 2.2 mm. Therefore, the amplitude at the location P11 was minimum, while the amplitude at the location P9 was maximum. Also, the amplitudes at the locations P10 and P12 were medium.
The amplitude at the location P13 is smaller than the amplitude at the location P9, because the coupling bar 5-2 is located at the location P13 to suppress the vibration of the portion of the semi-circular piezoelectric actuator 3-2 at the location P13. That is, if no coupling bar is present at the location P13, the amplitude at the location P13 would be considered to be the same as the amplitude at the location P9, i.e., larger than 2.2 mm.
As is understood from FIG. 2, the amplitudes at the locations P1, P2, . . . , P16 of the circumferential line L in a resonant state can be as shown in FIG. 3. Thus, although the amplitudes at the locations P1, P9, P10 and P16 are opposite in phase to those at the locations P12, P13 and P14, a drive voltage VY1 is applied to the entire semi-circular piezoelectric actuator 3-1. Also, although the amplitudes at the locations P1, P2, P8 and P9 are opposite in phase to those at the locations P4, P5 and P6, a drive voltage VY2 opposite in phase to the drive voltage VY1 is applied to the entire semi-circular piezoelectric actuator 3-2. As a result, the drive power by the drive voltages VY1 and VY2 would be decreased.
FIG. 4 is a perspective view illustrating a second prior art one-dimensional optical deflector (see: FIGS. 26, 27, 28 and 29 of JP2010-197994A and US2010/0195180A1).
As illustrated in FIG. 4, the second prior art one-dimensional optical deflector is constructed by a circular mirror 101, a pair of torsion bars 102a and 102b arranged along a Y-axis each having an end coupled to the circumference of the mirror 101, a pair of linear piezoelectric actuators 103a-1 and 103a-2 each having an end coupled to the torsion bar 102a, a pair of linear piezoelectric actuators 103b-1 and 103b-2 each having an end coupled to the torsion bar 102b, and a rectangular fixed frame 104 coupled to other ends of the linear piezoelectric actuators 103a-1, 103a-2, 103b-1 and 103b-2.
In FIG. 4, piezoelectric portions 103a-11, 103a-21, 103b-11 and 103b-21 made of PZT are formed on only two-thirds of the linear piezoelectric actuators 103a-1, 103a-2, 103b-1 and 103b-2, respectively. That is, if a length between the torsion bar 102a (102b) and the fixed frame 4 is L, the piezoelectric portions 103a-11, 103a-21, 103b-11 and 103b-21 are formed in length portions having a length LP (=2L/3) from the torsion bar 102a (102b). In this case, a drive voltage VY1 is applied to the piezoelectric portions 103a-11 and 103b-11, while a drive voltage VY2 opposite in phase to the drive voltage VY1 is applied to the piezoelectric portions 103a-21 and 103b-21. Thus, the rocking angle of the mirror 1 can be maximum under the same drive voltages VY1 and VY2.
FIG. 5 is a perspective view illustrating a third prior art one-dimensional optical deflector (see: FIGS. 30, 31, 32, 33 and 34 of JP2010-197994A and US2010/0195180A1).
In FIG. 5, further piezoelectric portions 103a-12, 103a-22, 103b-12 and 103b-22 separated from the piezoelectric portions 103a-11, 103a-21, 103b-11 and 103b-21 are formed on the linear piezoelectric actuators 103a-1, 103a-2, 103b-1 and 103b-2, respectively, of FIG. 4. In this case, the drive voltage VY1 is applied to the piezoelectric portions 103a-22 and 103b-22, while the drive voltage VY2 is applied to the piezoelectric portions 103a-12 and 103b-12. Thus, the rocking angle of the mirror 1 can be further increased under the same drive voltages VY1 and VY2.
In FIGS. 4 and 5, the length LP of the piezoelectric portions 103a-11, 103a-21, 103b-11 and 103b-22 is determined in accordance with the maximum value of the flexing angle of the linear piezoelectric actuators 103a-1, 103a-2, 103b-1 and 103b-2 when no torsion bar is coupled thereto or the maximum value of the moment of the linear piezoelectric actuators 103a-1, 103a-2, 103b-1 and 103b-2 when the torsion bars 102a and 102b are fixed.
Therefore, even if the one-dimensional optical deflector of FIG. 1 is combined with the one-dimensional optical deflector of FIG. 4 or 5, the drive power cannot always be increased. As a result, the drive power cannot be increased and the reliability cannot be enhanced.